A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation

TL;DR

This paper introduces a new dynamical low-rank scheme for the Vlasov equation that conserves mass, momentum, and energy, addressing a key challenge in high-dimensional kinetic simulations.

Contribution

The authors develop a conservative dynamical low-rank algorithm that preserves physical quantities and can be integrated with conservative discretizations.

Findings

Conserves mass, momentum, and energy in simulations.

Reduces computational cost of solving the Vlasov equation.

Compatible with conservative discretization methods.

Abstract

The primary challenge in solving kinetic equations, such as the Vlasov equation, is the high-dimensional phase space. In this context, dynamical low-rank approximations have emerged as a promising way to reduce the high computational cost imposed by such problems. However, a major disadvantage of this approach is that the physical structure of the underlying problem is not preserved. In this paper, we propose a dynamical low-rank algorithm that conserves mass, momentum, and energy as well as the corresponding continuity equations. We also show how this approach can be combined with a conservative time and space discretization.